Estimating and using slowness vector attributes in connection with a multi-component seismic gather

ABSTRACT

A technique includes determining at least one attribute of a slowness vector associated with a seismic gather based on pressure data and an indication of particle motion that is measured by at least one seismic sensor while in tow.

BACKGROUND

The invention generally relates to estimating and using slowness vectorattributes in connection with a multi-component seismic gather.

Seismic exploration involves surveying subterranean geologicalformations for hydrocarbon deposits. A survey typically involvesdeploying seismic source(s) and seismic sensors at predeterminedlocations. The sources generate seismic waves which propagate into thegeological formations creating pressure changes and vibrations alongtheir way. Changes in elastic properties of the geological formationscatter the seismic waves, changing their direction of propagation andother properties. Part of the energy emitted by the sources reaches theseismic sensors. Some seismic sensors are sensitive to pressure changes(hydrophones), others to particle motion (geophones), and industrialsurveys may deploy only one type of sensors or both. In response to thedetected waves, the sensors generate electrical signals to produceseismic data. Analysis of the seismic data can then indicate thepresence or absence of probable locations of hydrocarbon deposits.

Some surveys are known as “marine” surveys because they are conducted inmarine environments. However, “marine” surveys may be conducted not onlyin saltwater environments, but also in fresh and brackish waters. In afirst type of marine survey, called a “towed-array” survey, an array ofstreamers and sources is towed behind a survey vessel. In a second typeof marine survey, an array of seismic cables, each of which includesmultiple sensors, is laid on the ocean floor, or sea bottom; and asource is towed behind a survey vessel.

Historically, towed-array seismic surveys only employed pressure waves,and the sensors detected passing pressure wavefronts. The art hasrecently begun moving to “multi-component” surveys in which the sensorsalso detect particle velocities.

SUMMARY

In an embodiment of the invention, a technique includes determining atleast one attribute of a slowness vector associated with a seismicgather based on pressure data and data indicative of particle motion,which are measured by at least one seismic sensor while in tow.

In another embodiment of the invention, a system includes an interfaceand a processor. The interface receives pressure data and dataindicative of particle motion, which are measured by at least oneseismic sensor in tow. The processor determines at least one attributeof a slowness vector associated with a seismic gather based on thepressure data and particle motion data.

In yet another embodiment of the invention, an article includes acomputer accessible storage medium to store instructions that whenexecuted by a processor-based system causes the processor-based systemto determine at least one attribute of a slowness vector associated witha seismic gather based on pressure data and data indicative of particlemotion, which are measured by at least one seismic sensor while in tow.

Advantages and other features of the invention will become apparent fromthe following drawing, description and claims.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a schematic diagram of a marine seismic acquisition systemaccording to an embodiment of the invention.

FIG. 2 illustrates the geometry associated with a common midpointseismic gather according to an embodiment of the invention.

FIG. 3 is an illustration of exemplary traces associated with a seismicgather.

FIG. 4 is an illustration of primary and free surface multiple events.

FIG. 5 is a perspective view of a pressure wave illustrating thedefinition of a local slope according to an embodiment of the invention.

FIGS. 6 and 7 are flow diagrams depicting techniques to estimate thelocal slope from multi-component measurements according to embodimentsof the invention.

FIG. 8 depicts plots of the local slope as obtained from a mathematicalmodel and estimated from a synthesized seismic gather.

FIG. 9 is a flow diagram depicting a technique to improve detection of aseismic event according to an embodiment of the invention.

FIG. 10 is a flow diagram depicting a technique to use a slowness vectorestimate to remove noise according to an embodiment of the invention.

FIG. 11 is a flow diagram depicting a technique to use a slowness vectorestimate to replace measurements associated with interpolation accordingto an embodiment of the invention.

FIG. 12 is a flow diagram depicting a technique to use a slowness vectorestimate in a filtering application according to an embodiment of theinvention.

FIG. 13 is a flow diagram depicting a technique to use a slowness vectorestimate in a deghosting application according to an embodiment of theinvention.

FIG. 14 is a flow diagram depicting a technique to use a slowness vectorestimate to rotate the coordinate frame associated with velocitymeasurements according to an embodiment of the invention.

FIG. 15 is a flow diagram depicting a technique to use a slowness vectorestimate to estimate errors in a velocity model or indicate non-primaryevents according to an embodiment of the invention.

FIG. 16 is a flow diagram depicting a technique to use a slowness vectorestimate in an image processing application according to an embodimentof the invention.

FIG. 17 is a schematic diagram of a seismic data processing systemaccording to embodiments of the invention.

DETAILED DESCRIPTION

FIG. 1 depicts an embodiment 10 of a marine seismic data acquisitionsystem in accordance with some embodiments of the invention. In thesystem 10, a survey vessel 20 tows one or more seismic streamers 30 (oneexemplary streamer 30 being depicted in FIG. 1) behind the vessel 20.The seismic streamers 30 may be several thousand meters long and maycontain various support cables (not shown), as well as wiring and/orcircuitry (not shown) that may be used to support communication alongthe streamers 30.

Each seismic streamer 30 contains multi-component seismic sensors 58,each of which is capable of detecting a pressure wavefield and at leastone component of a particle motion that is associated with acousticsignals that are proximate to the multi-component seismic sensor 58.Examples of particle motions include one or more components of aparticle displacement, one or more components (inline (x), crossline (y)and depth (z) components, for example) of a particle velocity and one ormore components of a particle acceleration.

Depending on the particular embodiment of the invention, themulti-component seismic sensor 58 may include one or more hydrophones,geophones, particle displacement sensors, particle velocity sensors,accelerometers, or combinations thereof.

For example, in accordance with some embodiments of the invention, aparticular multi-component seismic sensor 58 may include a hydrophone 55for measuring pressure and three orthogonally-aligned accelerometers 50to measure three corresponding orthogonal components of particlevelocity and/or acceleration near the seismic sensor 58. It is notedthat the multi-component seismic sensor 58 may be implemented as asingle device (as depicted in FIG. 1) or may be implemented as aplurality of devices, depending on the particular embodiment of theinvention.

In accordance with some embodiments of the invention, the towedstreamers may be a densely sampled point receiver system.

The marine seismic data acquisition system 10 includes one or moreseismic sources 40 (one exemplary source 40 being depicted in FIG. 1),such as air guns and the like. In some embodiments of the invention, theseismic sources 40 may be coupled to, or towed by, the survey vessel 20.Alternatively, in other embodiments of the invention, the seismicsources 40 may operate independently of the survey vessel 20, in thatthe sources 40 may be coupled to other vessels or buoys, as just a fewexamples.

As the seismic streamers 30 are towed behind the survey vessel 20,acoustic signals 42 (an exemplary acoustic signal 42 being depicted inFIG. 1), often referred to as “shots,” are produced by the seismicsources 40 and are directed down through a water column 44 into strata62 and 68 beneath a water bottom surface 24. The acoustic signals 42 arereflected from the various subterranean geological formations, such asan exemplary formation 65 that is depicted in FIG. 1.

The incident acoustic signals 42 that are generated by the sources 40produce corresponding reflected acoustic signals, or pressure waves 60,which are sensed by the multi-component seismic sensors 58. It is notedthat the pressure waves that are received and sensed by the seismicsensors 58 may be primary pressure waves that propagate to the sensors58 without reflection, as well as secondary pressure waves that areproduced by reflections of the pressure waves 60, such as pressure wavesthat are reflected from an air-water boundary 31.

In accordance with some embodiments of the invention, the seismicsensors 58 generate signals (digital signals, for example), called“traces,” which indicate the detected pressure waves. The traces arerecorded and may be at least partially processed by a signal processingunit 23 that is deployed on the survey vessel 20, in accordance withsome embodiments of the invention. For example, a particularmulti-component seismic sensor 58 may provide a trace, which correspondsto a measure of a pressure wavefield by its hydrophone 55 and mayprovide one or more traces, which correspond to one or more componentsof particle motion, which are measured by its accelerometers 50.

The goal of the seismic acquisition is to build up an image of a surveyarea for purposes of identifying subterranean geological formations,such as the exemplary geological formation 65. Subsequent analysis ofthe representation may reveal probable locations of hydrocarbon depositsin the subterranean geological formations. Depending on the particularembodiment of the invention, portions of the analysis of therepresentation may be performed on the seismic survey vessel 20, such asby the signal processing unit 23. However, in accordance with otherembodiments of the invention, the representation may be furtherprocessed by a seismic data processing system (such as an exemplaryseismic data processing system 600 that is depicted in FIG. 17 andfurther described below) that may be, for example, located on land.Thus, many variations are possible and are within the scope of theappended claims.

Seismic data that shares a common geometry, called a gather, isprocessed for purposes of determining information about a particularspot of the survey area. As a more specific example, FIG. 2 depicts ageometry 100 of an exemplary common midpoint (CMP) seismic gatheraccording to some embodiments of the invention. The seismic gather maybe processed to yield information about a midpoint 118 of the geometry100. In the course of acquiring seismic data, the towed streamers 30(see also FIG. 1) acquire many such CMP midpoint gathers, for purposesof obtaining information about other points of the survey area.

The traces that are obtained from the CMP seismic gather may be stackedtogether, for purposes of improving the signal-to-noise ratio of themeasurement. However, before traces of the seismic gather are stacked orotherwise processed, the traces may first be aligned in time (called“moveout correction”) to account for different source-to-receiveroffsets that are present in the geometry 100.

More specifically, the geometry 100 is formed from differentsource-receiver pairs that share the midpoint 118 in common. FIG. 2depicts three exemplary source positions 120 a, 120 b and 120 c andthree corresponding exemplary receiver positions 122 a, 122 b and 122 c.The receiver and source positions correspond to various positions of thesources 40 (see FIG. 1) and multi-component sensors 58 (see FIG. 1)during the towing of the streamers 30.

The source positions 120 a, 120 b and 120 c are associated with thereceiver positions 122 a, 122 b and 122 c, respectively. As can be seenfrom FIG. 2, each source-receiver pair is separated by a differentdistance, or offset. This offset, in turn, directly affects the time fora signal to propagate from the source position to the receiver position.

For example, from the source position 120 a, the shot propagates througha path 102 to the midpoint 118, where a corresponding reflected pressurewave is produced, which propagates along a path 104 to the receiverposition 122 a. The shot that propagates from the source position 120 bfollows a shorter path, in that the shot propagates along a path 106 tothe midpoint 118 to produce a corresponding reflection wave thatpropagates along a path 108 to the receiver position 122 b. The offsetbetween the source position 120 c and receiver position 122 c is thesmallest possible, as a shot propagates from the source position 120 calong a path 110 to the midpoint 118 to produce a correspondingreflection wave that propagates along a path 112 to the receiverposition 122 c.

Thus, the trace that is associated with the receiver position 122 c isassociated with the smallest propagation time, and the trace that isassociated with the receiver position 122 a is associated with thelongest propagation time.

As a result of the different source-receiver offsets, the correspondingtraces of the gather are offset in time with respect to each other. Forexample, referring to FIG. 3 in conjunction with FIG. 2, the sensors 50(FIG. 1) that are associated with pressure waves at the receiverpositions 122 c, 122 b and 122 a produce corresponding traces 150 a, 150b and 150 c, which are depicted in FIG. 3. As shown, each of the traces150 a, 150 b and 150 c are offset in time with respect to each other,corresponding to the different source-to-receiver offsets. The timingbetween the traces 150 a, 150 b and 150 c follows a moveout curve 160,which may be represented by a mathematical function (a hyperbolicfunction, for example).

Traditionally, velocity analysis has been applied to measured pressuredata for purposes of selecting a mathematical formula-based modelmovement curve that characterizes the timing between the traces 150 a,150 b and 150 c; and the data in a seismic gather is time-shifted in aprocess (called “moveout correction”) based on the model moveout curve.Therefore, the choice of the mathematical function that forms the modelmoveout curve typically significantly affects the overall quality of theprocessed seismic data.

A characterizing parameter of the moveout curve is its “local slope,”which is the inline component of the slowness vector (also called thedirection of propagation vector) of the detected pressure wavefield. Ingeneral, the slowness vector (at the receiver) may be represented interms of inline (x), crossline (y) and depth (z) coordinates, and time(t) as follows:

$\begin{matrix}{{{Slowness\_ vector} = {{\frac{\partial t}{\partial x}\hat{x}} + {\frac{\partial t}{\partial y}\hat{y}} + {\frac{\partial t}{\partial z}\hat{z}}}},} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

Thus, the local slope, called “p_(x)” herein, is equal to the inline (x)component of the (receiver-side) slowness vector, or

$\frac{\partial t}{\partial x}.$A similar definition applies in common receiver gathers for thesource-side slowness vector.

In accordance with embodiments of the invention described herein, themulti-component data (i.e., pressure and particle velocity data) that isobtained via the towed streamers 30 is processed to obtain estimates ofthe local slope independently from the model moveout curve; and asdescribed below, these estimates may be used to evaluate the model curvefor purposes of seismic event detection.

As further described below, estimates of one or more components of theslowness vector may be used for purposes other than moveout correction.For example, an estimate of the slowness vector may be used to remove“multiples,” which are caused by reflections. A potential scenario inwhich multiples may occur is depicted in FIG. 4. The slowness vector(called “p_(s)”) at a source 180 and the slowness vector (called“p_(r)”) at a receiver 184 may be used for purposes of discriminatingprimary waves from reflected waves, as the primary and reflected wavesmay have the same travel time between the source 180 and the receiver184 but are distinguished by their associated slowness vectors.

As depicted in FIG. 4, a primary wave may follow a primary raypath 181from the source 180 to a midpoint 192 at the water bottom surface 24where the primary wave is reflected along a raypath 182 to the receiver184. The same shot from the source 180 may produce a secondary wave thatfollows a raypath 185 to a point 194 at which the wave is reflected toproduce a wave along a wave path 186. As shown in FIG. 4, this wave isreflected at a point 199 at the air-water surface 31 to produce acorresponding reflected wave that propagates along a raypath 184 toanother point 195, which produces a reflected wave that propagates alongthe raypath 188 to the receiver 184. As depicted in FIG. 4, the sourcep_(s) and receiver p_(r) slowness vectors may be used to distinguish theprimary from the secondary waves, although the primary and secondarywaves have the same travel time.

Other applications that benefit from estimating attributes of theslowness vector estimate are described below.

The components of the slowness vector may be estimated from timederivatives of the measured pressure and particle velocity data (i.e.,the multi-component data). More specifically, assume a pressure wave isrepresented by the function P(x, y, z, t), where “x” represents thein-line direction, “y” represents the cross-line direction, “z”represents the vertical direction and “t” represents time. In seismicmulti-component acquisitions, the spatial derivatives of the P(x, y, z,t) function may be directly calculated from the measured particlevelocities. For example, the partial derivative of the P(x, y, z, t)function with respect to the in-line direction may be represented asfollows:

$\begin{matrix}{{\frac{\partial{P\left( {x,y,z,t} \right)}}{\partial x} = {\rho{{\overset{.}{V}}_{x}\left( {x,y,z,t} \right)}}},} & {{Eq}.\mspace{14mu} 2}\end{matrix}$where “ρ” represents the density of the medium (assumed to behomogeneous); and “{dot over (V)}_(x)” represents the time derivative ofthe measured particle velocity V_(x)(x, y, z, t) (i.e., the inline(x)component of the measured particle velocity). As another example, thepartial derivative of the P(x, y, z, t) function with respect to thecross-line direction may be calculated as follows:

$\begin{matrix}{{\frac{\partial{P\left( {x,y,t} \right)}}{\partial y} = {\rho{{\overset{.}{V}}_{y}\left( {x,y,t} \right)}}},} & {{Eq}.\mspace{14mu} 3}\end{matrix}$where “{dot over (V)}_(y)(x,y,t)” represents the time derivative of themeasured particle velocity V_(y)(x,y,t) (i.e., the crossline (y)component of the measured particle velocity).

Given the above-described relationships between the time and spatialderivatives, the components of the slowness vector may be calculated asfollows, with a specific example being illustrated in FIG. 5 for anexemplary two-dimensional (2-D) pressure function P(x,t). The P(x,t)function is illustrated in FIG. 5 by an exemplary pressure wave 200. Atpoint ( x, t) (at reference numeral 206) the associated slowness vectorhas an inline component, or local slope, which is parallel to a line210. By

representing the time derivative of the P(x,t) function as

${P_{t}\left( {x,t} \right)} = {\overset{.}{P} = \frac{\partial P}{\partial t}}$and the spatial derivative of the P(x,t) function by

${{P_{x}\left( {x,t} \right)} = \frac{\partial P}{\partial x}},$a tangent plane 204 may be represented by a function π, which isdescribed by the following linear equation:π:|z(x,t)=P _(x)( x, t )(x− x )+P _(t)( x, t )(t− t )+P( x, t ).  Eq. 4

The local slope of the P(x,t) function at the point( x, t) may beidentified using the line 210, a line that is tangent at ( x, t) to theP(x,t) function and is parallel to the horizontal plane 225 (z= z=P( x,t)). The line 210 is obtained as the intersection between the tangentplane 204 and the pressure wave 200. Mathematically, the line 210 may berepresented by a function r, which is set forth below:

$\begin{matrix}{{\left. {r\text{:}} \middle| {t\left( {x,\overset{\_}{z}} \right)} \right. = {{{- \frac{P_{x}\left( {\overset{\_}{x},\overset{\_}{t}} \right)}{P_{t}\left( {\overset{\_}{x},\overset{\_}{t}} \right)}}\left( {x - \overset{\_}{x}} \right)} + \overset{\_}{t}}},} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

The local slope, or the slope of the line 210 may be represented by afunction m(x,t), as follows:

$\begin{matrix}{{m\left( {x,t} \right)} = {\frac{\partial t}{\partial x} = {- {\frac{P_{x}\left( {x,t} \right)}{P_{t}\left( {x,t} \right)}.}}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

In terms of the available multi-component data, Eq. 6 may be rewrittenas follows:

$\begin{matrix}{{{m\left( {x,t} \right)} = \frac{\rho{{\overset{.}{V}}_{x}\left( {x,t} \right)}}{\overset{.}{P}\left( {x,t} \right)}},} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

Referring to FIG. 6, to summarize, in accordance with some embodimentsof the invention, a technique 250 includes receiving pressure wave andparticle velocity data that are associated with a multi-componentseismic gather, pursuant to block 252. Estimates of slowness vectorattributes (such as local slope) may then be estimated (block 256) basedon the pressure wave and particle velocity data.

More specifically, in accordance with some embodiments of the invention,a technique 280 that is depicted in FIG. 7 may be used for purposes ofdetermining the local slope. Pursuant to the technique 280, particlevelocity and pressure data is accessed (block 284); and the spatialderivatives of the pressure are determined based on the particlevelocities, pursuant to block 288. Next, the time derivative of thepressure is determined (block 292); and subsequently the local slope inthe time-space domain is determined (block 296) based on the spatialderivative pressure and the time derivative of pressure.

It is noted that crossline (y) and depth (z) components of the slownessvector may be estimated in a similar manner.

FIG. 8 depicts a plot 304 of estimated local slopes obtained from datathat was produced in a synthesized multi-component seismic gatherpursuant to the techniques that are described above. As can been seen,the plot 304 closely matches a local slope curve 300, which is derivedfrom a mathematical formula-based model moveout curve.

The estimation of the slowness vector from the multi-component (particlemotion and pressure) measurements is a departure from the traditionalscheme of estimating the slowness vector, in which only pressuremeasurements are used. More specifically, the traditional technique forestimating the slowness vector is the local slant stack. Plane-waveannihilation filters may be applied, such as the one set forth below inEq. 8 for purposes of obtaining better estimates using this traditionalapproach:

$\begin{matrix}{{{{p_{x}\frac{\partial P}{\partial t}} + \frac{\partial P}{\partial x}} \approx 0},{{{{or}\mspace{14mu} p_{x}\frac{\partial P}{\partial t}} + \frac{\partial P}{\partial t}} \approx 0},} & {{Eq}.\mspace{14mu} 8}\end{matrix}$

Slowness vector components may be obtained from Eq. 8 by minimizing theresiduals (i.e., the right hand side of the equation) in a least squaressense. More specifically, the slowness vectors may be estimated forinterfering plane waves by convolutions of plane wave annihilationfilters. In this regard, a wave field that is the sum of two plane wavesis annihilated by the convolution of the annihilation filters for eachof the two plane waves.

The traditional techniques, if applied to three-dimensional (3-D) marineacquisition, are strongly subject to leakage in crossline direction.Because these traditional techniques stack the coherence of data alongknown curves, the modeling of such curves is a key factor for thequality of the analysis results.

The estimation of the local slope from multi-component data may be usedto evaluate the reliability of the events that are detected bytraditional techniques and may be used to reduce the leakage in thecrossline direction.

More specifically, traditional techniques evaluate coherency using asemblance formulation, called “S(x₀, q, t₀),” such as the following:

$\begin{matrix}{{{S\left( {x_{0},q,t_{0}} \right)} = \frac{\left\lbrack {\sum\limits_{k = 1}^{N_{k}}\;{P\left( {{t = \sqrt{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}^{2}}},x_{k}} \right)}} \right\rbrack^{2}}{N_{k}\left\lbrack {\sum\limits_{k = 1}^{N_{k}}\;{P\left( {t = \sqrt{{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}^{2}},x_{k}}} \right)}^{2}} \right\rbrack}},} & {{Eq}.\mspace{14mu} 9}\end{matrix}$where “t₀” is the zero-offset travel-time, “q” is the curvature, “x₀” isthe curve-apex position, “x_(k)” is the k-th receiver position, and“N_(k)” is the number of receivers.

The S(x₀, q, t₀) semblance formulation evaluates the coherency of themeasured pressure data along the following hyperbolic moveout curve:t(x,t ₀ ,q,x ₀)=√{square root over (t ₀ ² +q(x−x ₀)²)},  Eq. 10which has the following local slope:

$\begin{matrix}{{m\left( {x,t_{0},q,x_{0}} \right)} = {\frac{\partial t}{\partial x} = {\frac{q\left( {x - x_{0}} \right)}{\sqrt{t_{0}^{2} + {q\left( {x - x_{0}} \right)}^{2}}}.}}} & {{Eq}.\mspace{14mu} 11}\end{matrix}$

Thus, if a seismic event is matched by the modeled curve (Eq. 10), thenthe estimated local slopes of the measured pressure signal along thecurve should match the values obtained from Eq. 11.

An operator called Sl_(MSE)(x₀, q, t₀) may be used to evaluate how theslopes of the detected event respect their theoretical values (i.e.,values obtained from Eq. 11). The Sl_(MSE)(x₀, q, t₀) operatorcalculates a mean square error (MSE) between these slopes and isnormalized with respect to the mean square theoretical slope. TheSl_(MSE)(x₀, q, t₀) operator may be described as follows:

$\begin{matrix}{{{{Sl}_{MSE}\left( {x_{0},q,t_{0}} \right)} = \frac{\left( \left( {{\sum\limits_{k = 1}^{N_{k}}\;\frac{q\left( {x_{k} - x_{0}} \right)}{\sqrt{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}^{2}}}} + \frac{\rho{{\overset{.}{V}}_{x}\left( {{t = \sqrt{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}^{2}}},x_{k}} \right)}}{\overset{.}{P}\left( {{t = \sqrt{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}^{2}}},x_{k}} \right)}} \right)^{2} \right)}{\left( {\sum\limits_{k = 1}^{N_{k}}\;\left( \frac{q\left( {x_{k} - x_{0}} \right)}{\sqrt{t_{0}^{2} + {q\left( {x_{k} - x_{0}} \right)}}} \right)} \right)}},} & {{Eq}.\mspace{14mu} 12}\end{matrix}$

Another operator called R(x₀, q, t₀) may be used for purposes ofdetecting events that exhibit high semblance and low slope errors. TheR(x₀, q, t₀) operator may be described as follows:

$\begin{matrix}{{{R\left( {x_{0},q,t_{0}} \right)} = \frac{\lambda\;{S\left( {x_{0},q,t_{0}} \right)}}{\lambda + {{Sl}_{MSE}\left( {x_{0},q,t_{0}} \right)}}},} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

where “λ” has the role to balance the influence of S and Sl_(MSE), andmay also be used to mute or reduce the effect of the Sl_(MSE) operatorwhen it is expected to be too noisy.

The above-described techniques may be extended to the third dimension inthe case of three-dimensional (3-D) datasets, and the above-describedtechniques may be applied to different modeling domains, alternative tothe hyperbolic parameters (x₀, q, t₀).

Referring to FIG. 9, to summarize, the direct calculation of the localslope from the multi-component data may be used to improve the detectionof seismic events pursuant to a technique 400. In this regard, aparticular seismic event may be captured by multi-component data; and amoveout curve is selected, pursuant to block 402. A coherency of themeasured pressure data is calculated (block 406) along the moveoutcurve; and a mean error between the slopes is calculated directly fromthe multi-component data and the slopes predicted by the moveout curveare calculated (block 409). The reliability of the detected event isthen evaluated based on the calculated coherency and mean error,pursuant to block 412.

Estimates of the slowness vector may be obtained from themulti-component data, recognizing the concept of upgoing and downgoingvertical velocity components. In this regard, the downgoing verticalvelocity may be described as follows:

$\begin{matrix}{{D^{Vz} = {\frac{1}{2}\left( {V_{z} + {\frac{p_{z}}{\rho}P}} \right)}},} & {{Eq}.\mspace{14mu} 14}\end{matrix}$

In a similar manner, the upgoing V_(z) vertical velocity may bedescribed as follows:

$\begin{matrix}{{U^{Vz} = {\frac{1}{2}\left( {V_{z} - {\frac{p_{z}}{\rho}P}} \right)}},} & {{Eq}.\mspace{14mu} 15}\end{matrix}$

An algebraic combination of Equations 14 and 15 produces the followingestimator for the slowness vector based on the upgoing and downgoingV_(z) velocity measurements:Pp _(z)=ρ(D ^(Vz) −U ^(Vz)),  Eq. 16

Thus, Eq. 16 is an example of a technique to estimate the slownessvector based on upgoing and downgoing waves. The equation may beimplemented in space-time, leading to a system of equations to be solvedfor slowness vector. It is noted that the inline (x) component of theslowness vector may be derived from the p_(z) component due to thefollowing relationship:p^V=0, e.g., p _(x) V _(z) −p _(z) V _(z)=0,  Eq. 17

Equation 17 is based on the fact that the cross product of the velocityand slowness vectors is zero, due to the vectors being parallel to eachother.

For purposes of improving the slowness vector estimate, any of theabove-described techniques may be used in connection with frequencyranges that are associated with higher signal-to-noise ratios (SNRs).More specifically, referring to FIG. 10, in accordance with someembodiments of the invention, a technique 430 may be used for purposesof removing noise from multi-component seismic measurements. Pursuant tothe technique 430, the slowness vector is estimated (block 432) in afrequency range that has an associated sufficiently high signal-to-noiseratio (SNR), as compared to the other frequencies. It is assumed thatthe slowness vector is a broadband attribute. Therefore, in frequencybands in which the SNR is relatively low, the slowness vector estimateis used to improve the SNR at these frequencies, pursuant to block 436.More specifically, the slowness vector estimate is used to enforceconsistency between the multi-component measurements.

Besides being used to improve event detection and enforce consistencybetween multi-component measurements, the slowness vector estimates thatare derived from the multi-component data may have the followingadditional applications.

The spatial derivatives of the pressure wavefield may be used ininterpolation schemes. When the slowness vector estimate is available,the following relationship may be used to replace potentiallynoise-contaminated velocity measurements or pressure wavefield spacederivatives with pressure wave field time derivatives, as set forthbelow:

$\begin{matrix}{\frac{\partial P}{\partial x} = {{- p_{x}}{\frac{\partial P}{\partial t}.}}} & {{Eq}.\mspace{14mu} 18}\end{matrix}$

Thus, referring to FIG. 11, in accordance with some embodiments of theinvention, a technique 450 includes replacing (block 452)noise-contaminated velocity measurements and/or pressure wave fieldspace derivatives with pressure wavefield time derivatives, using theslowness vector estimate, pursuant to block 452.

In the course of seismic processing, it may be advantageous to computeplane wave or tau-p transforms. These transforms are usually performedby the summation of data along a range of pre-defined trajectories. Whenthe slowness vector estimate is available, the transforms may becomputed along the slowness vector direction. The resultant computationsare relatively fast and may have fewer transform-related artifacts thanthe artifacts that are produced via conventional techniques. Thus,referring to FIG. 12, in accordance with some embodiments of theinvention, a technique 460 includes computing (block 464) the plane waveor tau-p transform along the slowness vector direction, pursuant toblock 464.

Because the tau-p and Fourier transforms are related, theabove-described approach provides an alternative way of computingFourier transforms as well. Thus, following these transforms, events maybe separated according to their slowness vectors.

Referring to FIG. 13, in accordance with some embodiments of theinvention, a technique 470 may also use the slowness vector estimate forpurposes of obtaining a vertical wavenumber for three-dimensional (3-D)deghosting, pursuant to block 474.

Additionally, in accordance with some embodiments of the invention, theslowness vector estimate may be used for purposes of receiver-motioncorrections.

In accordance with some embodiments of the invention, the slownessvector estimate also permits transformations between coordinate spaces.For example, referring to FIG. 14, in accordance with some embodimentsof the invention, a technique 480 includes rotating (block 484) thevelocity measurement from a rectangular coordinate space to a coordinatespace that has an axis along the slowness vector.

Referring to FIG. 15, in accordance with some embodiments of theinvention, a technique 490 uses the slowness vector estimate forpurposes of indicating possible errors in a velocity model or indicatingnon-primary events, such as an event that is produced by a reflection ofthe primary event. More specifically, in accordance with someembodiments of the invention, the technique 490 includes using (block492) the slowness vector estimate to map events into a higherdimensional space (than the original data) that includes source andreceiver positions, as well as the slowness vectors. Thus, the estimatesof the slowness vector permit the mapping of the events into a higherdimensional space, which may include the source coordinates, receivercoordinates and time. These events may then be ray traced in the higherdimensional space, pursuant to block 494, and the ray tracing may beused to remove multiples (for example), pursuant to block 496.

Estimates of slowness vectors also allow for the map-migration ofevents, the testing of hypothesis for raypaths and interpretation ofpre-stack events. For example, map migration with constant velocity maybe used to identify locations of strong diffractors at the sea floor andfurther lead to suppression of multiple diffractions.

Referring to FIG. 16, in accordance with some embodiments of theinvention, a technique 500 is used for purposes of image processing.Pursuant to the technique 500, migration weights are determined (block502) of a velocity model using estimates of the slowness vector.

Referring to FIG. 17, in accordance with some embodiments of theinvention, a seismic data processing system 600 may perform one or moreof the above-described techniques to generate and use slowness vectorestimates. In accordance with some embodiments of the invention, thesystem 600 may include a processor 602, such as one or moremicroprocessors or microcontrollers. The processor 602 may be coupled toa communication interface 630 for purposes of receiving the pressurewave data and particle motion data. As examples, the communicationinterface 630 may be a USB serial bus interface, a network networkedinterface, a removable media (such as a flash card, CD-ROM, etc.)interface, or a magnetic storage interface (an IDE or SCSI interface, asjust a few examples). Thus, the communication interface 630 may take onnumerous forms, depending on the particular embodiment of the invention.

The communication interface 630 may be coupled to a memory 610 of thecomputer 600, which may, for example, store the pressure wave andparticle motion data as indicated at reference numeral 620, inaccordance with some embodiments of the invention. Additionally, thememory 610 may store at least one application program 614, which isexecuted by the processor 602 for purposes of estimating and usingattributes of the slowness vector pursuant to the techniques that aredisclosed herein. The memory 610 and communication interface 630 may becoupled together by at least one bus 640 and may be coupled by a seriesof interconnected buses and bridges, depending on the particularembodiment of the invention.

While the present invention has been described with respect to a limitednumber of embodiments, those skilled in the art, having the benefit ofthis disclosure, will appreciate numerous modifications and variationstherefrom. It is intended that the appended claims cover all suchmodifications and variations as fall within the true spirit and scope ofthis present invention.

What is claimed is:
 1. A method comprising: processing, on aprocessor-based system, pressure data and an indication of particlemotion measured by at least one seismic sensor while in tow wherein theprocessing determines at least one attribute of a slowness vectorassociated with a seismic gather based on a model of the at least oneattribute as a function of pressure and particle motion, the determiningcomprising determining a spatial derivative of the pressure data basedon the indication of the particle motion.
 2. The method of claim 1,further comprising processing the pressure data and the indication todetermine a change in a pressure travel time with respect to a receiveroffset.
 3. The method of claim 1, wherein the processing the pressuredata and the indication to determine further comprises: determining atime derivative of the pressure data; and basing the determination ofthe at least one attribute on the determination of the time derivativeof the pressure data and the determination of the spatial derivative ofthe pressure data.
 4. The method of claim 1, wherein the indication ofthe particle motion comprises an indication of a velocity.
 5. The methodof claim 1, wherein the processing comprises processing the pressuredata and the indication to determine a local slope, the method furthercomprising: determining a slope error based on the determined localscope and a mathematical model of the slope.
 6. The method of claim 5,further comprising: determining a seismic event reliability measurebased on the slope error.
 7. The method of claim 6, further comprising:further basing the seismic event reliability measure on asemblance-based coherency measure of the gather.
 8. The method of claim1, further comprising: determining the at least one attribute of theslowness vector from a frequency range in which an associatedsignal-to-noise ratio is higher than a signal-to-noise ratio of a secondfrequency range; and using the at least one attribute to improve aconsistency of the pressure data and the indication of particle motion.9. The method of claim 1, further comprising: determining a transformalong a direction of the slowness vector.
 10. The method of claim 1,further comprising: rotating a coordinate frame associated with theindication of particle motion to a coordinate frame that includes theslowness vector as an axis that is directed along the slowness vector.11. The method of claim 1, further comprising: removing multiples fromthe seismic gather based on the slowness vector.
 12. The method of claim1, further comprising: determining migration weights of a velocity modelbased on the slowness vector.
 13. The method of claim 1, wherein thedetermining the at least one component of the slowness vector comprises:determining an up going velocity based on the pressure wave data and theindication of particle motion; determining a down going velocity basedon the pressure wave data and the indication of particle motion; anddetermining the at least one attribute of the slowness vector inresponse to a combination of the up going and down going velocities. 14.The method of claim 1, further comprising: obtaining the pressure wavedata and the indication of particle motion from a densely sampled pointreceiver system.
 15. A system comprising: an interface to receivepressure data and an indication of particle motion measured by at leastone seismic sensor in tow; and a processor to determine at least oneattribute associated with a seismic gather based on a model of said atleast one attribute as a function of particle motion and pressure,wherein the determination of the at least one attribute includes theprocessor determining a spatial derivative of the pressure data based onthe indication of the particle motion.
 16. The system of claim 15,further comprising: at least one towed streamer comprising at least oneseismic sensor to indicate the pressure data.
 17. The system of claim16, wherein the at least one towed streamer comprises at least onemulti-component sensor to provide an indication of the particle motion.18. The system of claim 16, further comprising: at least one vessel totow the at least one towed streamer.
 19. The system of claim 15, whereinthe processor is adapted to determine a change in a pressure wave traveltime with respect to a receiver offset.
 20. The system of claim 15,wherein the processor is further adapted to: determine a time derivativeof the pressure data; and base the determination of the at least oneattribute on the determination of the time derivative of the pressuredata and the determination of the spatial derivative of the pressuredata.
 21. The system of claim 15, wherein the indication of the particlemotion comprises an indication of a velocity.
 22. The system of claim15, wherein the processor is adapted to determine a local slope errorbased on the at least one attribute of the slowness vector and amathematical model of the attribute.
 23. The system of claim 22, whereinthe processor is adapted to determine a seismic event reliabilitymeasure based on the slope error.
 24. The system of claim 23, whereinthe processor is adapted to further base the seismic event reliabilitymeasure on a semblance-based coherency measure of the gather.
 25. Thesystem of claim 15, wherein the processor is adapted to: determine theat least one attribute from a frequency range in which an associatedsignal-to-noise ratio is higher than a signal-to-noise ratio of a secondfrequency range; and use the at least one component to improve aconsistency of the pressure data and the indication of particle motion.26. The system of claim 15, wherein the processor is adapted to:determine a transform along a direction of the slowness vector.
 27. Thesystem of claim 15, wherein the processor is adapted to: rotate acoordinate frame associated with the indication of particle motion to acoordinate frame that includes the slowness vector as an axis that isdirected along the slowness vector.
 28. The system of claim 15, whereinthe processor is adapted to: remove multiples from the seismic gatherbased on the slowness vector.
 29. The system of claim 15, wherein theprocessor is adapted to: determine migration weights of a velocity modelbased on the slowness vector.
 30. The system of claim 15, wherein theprocessor is adapted to: determine an up going velocity based on thepressure data and the indication of particle motion; determine a downgoing velocity based on the pressure data and the indication of particlemotion; and determine the at least one attribute in response to acombination of the up going and down going velocities.
 31. The system ofclaim 15, wherein the pressure data and the indication of particlemotion are obtained from a densely sampled point receiver system.
 32. Anarticle comprising a non-transitory, computer-accessible, storage mediumto store instructions that when executed by a processor-based system,cause the processor-based system to: determine at least one attribute ofa slowness vector associated with a seismic gather based on a model ofsaid at least one attribute as a function of pressure and particlemotion, wherein the determination of the at least one attribute includesdetermining a spatial derivative of the pressure data based on theindication of the particle motion.
 33. The article of claim 32, thestorage medium storing instructions that when executed cause theprocessor-based system to determine a change in a pressure wave traveltime with respect to a receiver offset.
 34. The article of claim 32, thestorage medium storing instructions that when executed cause theprocessor-based system to: determine a time derivative of the pressurewave data; and base the determination of the at least one attribute onthe determination of the time derivative of the pressure wave data andthe determination of the spatial derivative of the pressure wave data.35. The article of claim 32, the storage medium storing instructionsthat when executed cause the processor-based system to determine localslope error based on the at least one attribute and a mathematical modelof the attribute.
 36. The article of claim 35, the storage mediumstoring instructions that when executed cause the processor-based systemto determine a seismic event reliability measure based on the slopeerror.
 37. The method of claim 1, wherein said at least one seismicsensor comprises multiple seismic sensors, the pressure data and theindication of particle motion are derived from traces acquired by themultiple seismic sensors, and the determination of said at least oneattribute of the slowness vector is performed independently from arelative timing of the traces with respect to each other.
 38. The systemof claim 15, wherein said at least one seismic sensor comprises multipleseismic sensors, the pressure data and the indication of particle motionare derived from traces acquired by the multiple seismic sensors, andthe determination of said at least one attribute of the slowness vectoris performed independently from a relative timing of the traces withrespect to each other.
 39. The article of claim 32, wherein said atleast one seismic sensor comprises multiple seismic sensors, thepressure data and the indication of particle motion are derived fromtraces acquired by the multiple seismic sensors, and the determinationof said at least one attribute of the slowness vector is performedindependently from a relative timing of the traces with respect to eachother.
 40. A method comprising: processing pressure data and anindication of particle motion measured by at least one seismic sensorwhile in tow on a processor-based system to determine at least oneattribute of a slowness vector associated with a seismic gather based onpressure data and an indication of particle motion measured by at leastone seismic sensor while in tow, the determining comprising determininga spatial derivative of the pressure data based on the indication of theparticle motion; and using the at least one attribute to replace aspatial derivative of a pressure wavefield in an interpolationdetermination.
 41. A system comprising: an interface to receive pressuredata and an indication of particle motion measured by at least oneseismic sensor in tow; and a processor to determine at least oneattribute associated with a seismic gather based on the pressure dataand the indication of the particle motion, wherein the determination ofthe at least one attribute includes the processor determining a spatialderivative of the pressure data based on the indication of the particlemotion, and the processor is adapted to use the at least one attributeto replace a spatial derivative of a pressure wavefield in aninterpolation determination.
 42. The method of claim 1, wherein thepressure data and the indication of particle motion are a seismicwavefield, and further comprising: based on the slowness vectorattribute, computing a vertical wavenumber of the seismic wavefield; andbased on the vertical wavenumber, the pressure data, and the indicationof particle motion, separating the seismic wavefield into an upgoingseismic wavefield and a downgoing seismic wavefield.
 43. The method ofclaim 42, further comprising performing deghosting on the seismicwavefield based on the upgoing seismic wavefield and the downgoingseismic wavefield.
 44. The method of claim 43, wherein the deghosting isthree-dimensional deghosting.
 45. The method of claim 1, wherein thepressure data and the indication of particle motion are a seismicwavefield, and further comprising: based on the slowness vectorattribute, computing a angle of incidence of the seismic wavefield; andbased on the angle of incidence, the pressure data, and the indicationof particle motion, separating the seismic wavefield into an upgoingseismic wavefield and a downgoing seismic wavefield.
 46. The method ofclaim 45, further comprising performing deghosting on the seismicwavefield based on the upgoing seismic wavefield and the downgoingseismic wavefield.
 47. The method of claim 46, wherein the deghosting isthree-dimensional deghosting.